How to put Login on homepage (maybe not what you think)

Hello WordPress experts. How can I put the Login FIELDS (Name / Password) on my sidebar? Not just the little link that says “Login” — I have that now, using this code:

<?php wp_register('', ' | '); ?> <?php wp_loginout(); ?>

The built-in Login page, while beautiful and wordpressy, breaks away from the visual theme of my site. I guess another option would be to style that page, but I thought it might be nice just to have the fields directly in my sidebar, kind of like the top of this forum when you’re not logged in. It might also encourage more people to register, not sure.

I checked out wp-login.php — whooooweee. Over my head. Not even sure where to start, whether find the code I need and put it in my sidebar, or some kind of “include” which I don’t know how to do.